Amanda Knox, convicted of murdering her British roommate Meredith Kercher, has nightmares and traumatic memories of her four years in Italian courts and prison. But she has only warm memories of Kercher and says she would like to visit her grave one day.

Knox talked about Kercher as well as her legal ordeal in an exclusive interview with ABC's Diane Sawyer. Her recall of those years has moments of regret, anger and sadness. Also among her emotions are warm thoughts of Kercher and empathy for her family.

"I want them to know," Knox said, getting emotional, "their grief has my every respect, has the respect of my family, and we just don't want to... we don't want to invade their life and their grief."

Watch Amanda Knox in an exclusive interview with Diane Sawyer set to air Tuesday at 10 p.m. ET.

"And I really want them to understand that my need for justice for myself is not in contradiction with theirs," she said.

Knox recalled her short time, a mere six weeks, with Kercher, who was also studying in Perugia.

"She talked about how she wanted to be a journalist like her dad. And she talked about her sister. And if that's all I can give them is this memory that I have of her to add to... all of theirs that they can carry with them when she's gone."

Knox paused at that point and added, "[I hope] that eventually I can have their permission to pay respects at her grave."

The Kercher family has made it clear they believe Knox is involved, but Knox's father, Curt, told Sawyer that he hopes the families can meet some day. "I would like to see them when they clearly, clearly understand that Amanda had nothing to do with the loss of their daughter."

The Kercher family has spoken only rarely in public about Meredith's death, but today her sister issued a statement saying they do not intend to read Knox's new memoir "Waiting to Be Heard."

"Meredith is the victim, and we are waiting to be heard," her sister Stephanie Kercher said.

Knox is still battling to convince the Italian judicial system -- and the world -- of her innocence. After nearly six years, Knox, with her freedom back on the line after a recent Supreme Court ruling ordering a new trial, is breaking her silence for the first time.

"I want the truth to come out. I want misunderstandings to be looked at. I would like to be re-considered as a person," Knox said.

In "Waiting to Be Heard," Knox writes about her conviction, life in prison, acquittal and how she has changed.

"I have been in an experience where I thought everything that I had hoped for in my life was taken away from me, and I had to redefine what mattered. And when I think about the purpose of what I wrote, I think about what I would tell my little sisters about how to live no matter what's stopping you," she said.

Knox's journey to study abroad in Perugia, Italy, in 2007 was care-free for only a six weeks before Kercher was murdered on Nov. 1.

Kercher had 47 wounds on her body, the deepest being a fatal slash to her throat. There were signs that Kercher, who was trained in karate, fought hard for her life.

"I was stunned by her death, completely bowled over because it was unfair. She was my friend, and I lost a friend," Knox said to Sawyer.

Now, nearly six years later, Knox concedes she is not the same person she was before the ordeal began, when she was 20. She thought her own personal hell was over when an Italian appeals court threw out her conviction and she came home to Seattle in 2011. But even before this latest ruling, the toll taken on her has been obvious.

"My family was expecting the old Amanda who was -- she makes goofy faces -- which was the old Amanda back. And I'm not quite as chirpy anymore."